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We are developing a large-scale reconfigurable data-path (LSRDP) based on single-flux-quantum (SFQ) circuits to establish a fundamental technology for future high-performance computing systems. In the LSRDP, an SFQ floating-point adder (FPA) is one of the main and most complicated circuit blocks. In this paper, we designed and implemented an SFQ half-precision FPA and carried out on-chip high-speed tests. The data format of the half-precision FPA obeys the IEEE standard, in which two input data streams, an 11-bit significand and a 6-bit sign/exponent, are processed bit-serially. The floating-point addition is performed by three steps: (1) alignment and rounding of significands, (2) addition/subtraction of the significands, and (3) normalization of the result. We implemented an SFQ half-precision FPA using the SRL 2.5 kA/cm2 niobium standard process. The size, power consumption and total junction number are 5.86 mm times 5.72 mm, 3.5 mW and 10224, respectively. The simulated DC bias margin is plusmn20% at 20 GHz operation, which corresponds to the performance of 1 GFLOPS. We successfully confirmed the correct operation of the FPA except a read-out circuit for the significand at 24 GHz by on-chip high-speed tests.